Axiomatization in Hilbert’s Early Career

Abstract

Having discussed the general, nineteenth-century background of Hilbert’s work, we can now focus more specifically on his axiomatic approach as it gradually consolidated over the last decade of the century. We will also see the way it was actually manifest in its earlier implementations. In this regard, I discuss in this chapter the following topics: Hilbert’s early lectures on geometry and mechanics (§ 2.1); the Grundlagen der Geometrie (§ 2.2) and its immediate sequels (§ 2.4); and the 1900 list of problems (§ 2.3).